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Concrete Abstract Algebra: From Numbers to Gröbner Bases

New. Sprache: Englisch.
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Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factorin … weiterlesen
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Concrete Abstract Algebra: From Numbers to Gröbner Bases als Buch

Produktdetails

Titel: Concrete Abstract Algebra: From Numbers to Gröbner Bases
Autor/en: Niels Lauritzen

ISBN: 0521826799
EAN: 9780521826792
New.
Sprache: Englisch.
CAMBRIDGE UNIV PR

Oktober 2003 - gebunden - 256 Seiten

Beschreibung

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a rich supply of topics such as cryptography, factoring algorithms for integers, quadratic residues, finite fields, factoring algorithms for polynomials, and systems of non-linear equations. A special feature is that Gr"obner bases do not appear as an isolated example. They are fully integrated as a subject that can be successfully taught in an undergraduate context. Lauritzen's approach to teaching abstract algebra is based on an extensive use of examples, applications, and exercises. The basic philosophy is that inspiring, non-trivial applications and examples give motivation and ease the learning of abstract concepts. This book is built on several years of experienced teaching introductory abstract algebra at Aarhus, where the emphasis on concrete and inspiring examples has improved student performance significantly.

Inhaltsverzeichnis

1. Numbers; 2. Groups; 3. Rings; 4. Polynomials; 5. Grobner bases.

Pressestimmen

'I highly recommend this book ... If you are looking for a solid introduction to the topic of abstract algebra, this is the book for you.' Computing Reviews 'A very useful book, which emphazises the relation between number theory and algebra offering also a very comprehensible introduction to a relatively new branch of algebra.' Monatshefte fur Mathematik '... this textbook is absolutely self-contained, with the prerequisites kept to a minimum. The exposition is perfectly lucid, rigorous, detailed and user-friendly, which makes the book also suitable for private study. In summary, this is a highly interesting and original textbook on basic abstract algebra, with many topical extras and didactic novelties. It is perfectly suited for beginners in the field...' Werner Kleinert, Zentralblatt MATH 'Unlike many books on abstract algebra, this one is written in a very lively style, with emphasis on illuminating examples and applications. This makes the book a valuable addition to undergraduate literature on this topical subject.' EMS Newsletter
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